represents a permutation with disjoint cycles .


  • The cycles of a permutation are given as lists of positive integers, representing the points of the domain in which the permutation acts.
  • A cycle represents the mapping of the to . The last point is mapped to .
  • Points not included in any cycle are assumed to be mapped onto themselves.
  • Cycles must be disjoint, that is, they must have no common points.
  • Cycles objects are automatically canonicalized by dropping empty and singleton cycles, rotating each cycle so that the smallest point appears first, and ordering cycles by the first point.
  • Cycles[{}] represents the identity permutation.
Introduced in 2010
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